Progress report

Exponents against the literature, the interval on every cell, what each discovery cost, and the evidence behind every bound.

Participate

Run it yourself, or point a coding agent at it.

git clone https://github.com/unitaryfoundation/stabrank
cd stabrank
# describe your decomposition in bounds/mybound.json
make fit BOUND=bounds/mybound.json ARGS=--write
make verify BOUND=bounds/mybound.json

fit solves for the exact coefficients, or tells you no exact combination of your terms reproduces the target. verify rebuilds the identity in exact arithmetic. If it passes, open a pull request adding the file and the leaderboard picks it up on the next build.

A bound the pipeline cannot check is recorded as cited and never takes a record.

← back to the board

Exponent comparison

Best record-tier exponent on the board against the published one. 4 beaten, 4 matched, 2 trailing or open.

orbitpublished γreferencebest herecelltiergapverdict
Strangequtrit0.3155Labib, Farrokh, Russo, Vincent (2026) arXiv:2605.285860.3155χ ≤ 2 at m=2lean0.0000matches
Norrellqutrit0.4206Labib, Farrokh, Russo, Vincent (2026) arXiv:2605.285860.4192χ ≤ 10 at m=5verified-0.0014beats
H₃qutrit0.4206Labib, Farrokh, Russo, Vincent (2026) arXiv:2605.285860.4206χ ≤ 4 at m=3lean0.0000matches
T₃qutrit0.5000Labib, Farrokh, Russo, Vincent (2026) arXiv:2605.285860.5000χ ≤ 3 at m=2lean0.0000matches
H-typequbit0.3962Qassim, Hammam, Pashayan, Hakop, Gosset, David (2021) arXiv:2106.077400.4170χ ≤ 18 at m=10lean+0.0208trails
BK T-typequbit0.3962Qassim, Hammam, Pashayan, Hakop, Gosset, David (2021) arXiv:2106.077400.3907χ ≤ 15 at m=10verified-0.0056beats
√Tqubit0.5000Qassim, Hammam, Pashayan, Hakop, Gosset, David (2021) arXiv:2106.077400.5121χ ≤ 12 at m=7verified+0.0121trails
CStwo-qubit1.0000none; single-copy product bound0.7925χ ≤ 3 at m=2verified-0.2075beats
T₅ququint0.6826none; single-copy product bound0.5000χ ≤ 5 at m=2lean-0.1826beats
magic catm qubits0.3962Qassim, Hammam, Pashayan, Hakop, Gosset, David (2021) arXiv:2106.077400.3962χ ≤ 3 at m=6verified0.0000matches

The published exponents are the four qutrit values of Labib, Farrokh, Russo, Vincent (2026) arXiv:2605.28586, for the H-type and T-type qubit orbits the contracted-cat-state exponent of Qassim, Hammam, Pashayan, Hakop, Gosset, David (2021) arXiv:2106.07740, and for √T the every-angle bound 1/2 of the same paper's Theorem 2. No exponent has been published for any p = 5 state or for the two-qubit CS orbit, so the T₅ baseline is the single-copy product bound log₅3 from χ(T₅) = 3 and the CS baseline is log₂2 = 1 from χ(CS) = 2. The gap is best minus published; negative would be an improvement. A match at the same rank replaces a cited value with a machine-checked one; it does not move the exponent.

Cell intervals

68 cells, 39 settled. 63 moved on or after 2026-09-15 (highlighted). Dates: provenance date, then the date the bound reached main when the two differ.

orbitmintervallower tierlower sinceupper tierupper sincestatus
Strange1χ = 2lean2026-09-20lean2026-05-27 · 2026-09-12settled
Strange2χ = 2lean2026-09-15 · 2026-09-16lean2026-05-27 · 2026-09-12settled
Strange3χ = 4reproduced2026-05-27 · 2026-09-12lean2026-05-27 · 2026-09-12settled
Strange4χ = 4reproduced2026-05-27 · 2026-09-12lean2026-05-27 · 2026-09-12settled
Strange56 ≤ χ ≤ 8attested2026-10-23lean2026-09-18open
Strange66 ≤ χ ≤ 8attested2026-10-23lean2026-05-27 · 2026-09-12open
Strange76 ≤ χ ≤ 16attested2026-10-23verified2026-09-22open
Strange86 ≤ χ ≤ 16attested2026-10-23verified2026-09-22open
Norrell1χ = 2verified2026-10-17 · 2026-10-21verified2026-10-17 · 2026-10-21settled
Norrell2χ = 3lean2026-09-12 · 2026-09-16lean2026-05-27 · 2026-09-12settled
Norrell3χ = 4reproduced2026-05-27 · 2026-09-12lean2026-05-27 · 2026-09-12settled
Norrell4χ = 7attested2026-09-26lean2026-05-27 · 2026-09-12settled
Norrell57 ≤ χ ≤ 10attested2026-10-17 · 2026-10-21verified2026-10-16 · 2026-10-17open
Norrell67 ≤ χ ≤ 16attested2026-10-17 · 2026-10-21verified2026-09-23open
H₃1χ = 2verified2026-10-17 · 2026-10-21verified2026-10-17 · 2026-10-21settled
H₃2χ = 3lean2026-09-12 · 2026-09-16lean2026-05-27 · 2026-09-12settled
H₃3χ = 4reproduced2026-05-27 · 2026-09-12lean2026-05-27 · 2026-09-12settled
H₃47 ≤ χ ≤ 8attested2026-10-02 · 2026-10-15lean2026-05-27 · 2026-09-12open
H₃57 ≤ χ ≤ 12attested2026-10-17 · 2026-10-21verified2026-09-23open
H₃67 ≤ χ ≤ 16attested2026-10-17 · 2026-10-21verified2026-09-23open
T₃1χ = 3lean2026-09-16lean2020-03-02 · 2026-09-12settled
T₃2χ = 3lean2026-09-07 · 2026-09-12lean2020-03-02 · 2026-09-12settled
T₃3χ = 8attested2026-09-20lean2026-05-27 · 2026-09-12settled
T₃48 ≤ χ ≤ 9attested2026-09-20lean2026-05-27 · 2026-09-12open
T₃58 ≤ χ ≤ 18attested2026-09-20lean2026-09-17open
T₃68 ≤ χ ≤ 27attested2026-10-17 · 2026-10-21verified2026-09-23open
H-type1χ = 2verified2026-10-17 · 2026-10-21verified2026-10-17 · 2026-10-21settled
H-type2χ = 2lean2026-09-20lean2015-06-03 · 2026-09-12settled
H-type3χ = 3reproduced2026-09-12 · 2026-09-16lean2015-06-03 · 2026-09-12settled
H-type4χ = 4reproduced2026-09-16 · 2026-09-17lean2026-05-27 · 2026-09-12settled
H-type5χ = 6attested2026-09-24 · 2026-09-23lean2015-06-03 · 2026-09-17settled
H-type6χ = 6attested2026-09-23 · 2026-09-22lean2021-06-14 · 2026-09-12settled
H-type76 ≤ χ ≤ 9attested2026-09-22lean2022-02-18 · 2026-09-21open
H-type86 ≤ χ ≤ 12attested2026-09-22lean2022-02-18 · 2026-09-21open
H-type96 ≤ χ ≤ 18attested2026-10-17 · 2026-10-21verified2026-09-22open
H-type106 ≤ χ ≤ 18attested2026-09-22lean2022-02-18 · 2026-09-21open
BK T-type1χ = 2verified2026-10-17 · 2026-10-21verified2026-10-17 · 2026-10-21settled
BK T-type2χ = 2lean2026-09-20lean2026-09-16 · 2026-09-17settled
BK T-type3χ = 3reproduced2026-09-16 · 2026-09-17lean2026-09-16 · 2026-09-17settled
BK T-type4χ = 3reproduced2026-09-12 · 2026-09-16lean2026-05-27 · 2026-09-12settled
BK T-type5χ = 6attested2026-09-24lean2026-09-18settled
BK T-type6χ = 6attested2026-09-24lean2026-05-27 · 2026-09-12settled
BK T-type76 ≤ χ ≤ 9attested2026-10-17 · 2026-10-21verified2026-10-17 · 2026-10-21open
BK T-type86 ≤ χ ≤ 9attested2026-10-17 · 2026-10-21verified2026-09-22open
BK T-type96 ≤ χ ≤ 15attested2026-10-17 · 2026-10-21verified2026-10-18 · 2026-10-21open
BK T-type106 ≤ χ ≤ 15attested2026-10-17 · 2026-10-21verified2026-10-12 · 2026-10-15open
√T1χ = 2verified2026-10-21verified2026-10-17 · 2026-10-21settled
√T2χ = 3verified2026-10-21verified2026-10-17 · 2026-10-21settled
√T3χ = 4verified2026-10-21verified2026-10-17 · 2026-10-21settled
√T4χ = 5verified2026-10-23 · 2026-10-24verified2026-10-17 · 2026-10-21settled
√T5χ = 6verified2026-10-23 · 2026-10-24verified2026-10-23 · 2026-10-24settled
√T67 ≤ χ ≤ 12attested2026-10-23 · 2026-10-24verified2026-10-23 · 2026-10-24open
√T77 ≤ χ ≤ 12attested2026-10-23 · 2026-10-24verified2026-10-23 · 2026-10-24open
CS1χ = 2verified2026-10-21verified2026-09-20 · 2026-10-21settled
CS2χ = 3verified2026-10-21verified2026-09-20 · 2026-10-21settled
CS34 ≤ χ ≤ 6reproduced2026-10-21verified2026-10-21open
T₅1χ = 3lean2026-09-21lean2026-09-20 · 2026-09-21settled
T₅2χ = 5reproduced2026-09-21lean2026-09-24settled
T₅36 ≤ χ ≤ 15attested2026-10-02 · 2026-10-15lean2026-09-24open
T₅46 ≤ χ ≤ 25attested2026-10-02 · 2026-10-15lean2026-09-24open
T₅56 ≤ χ ≤ 75attested2026-10-17 · 2026-10-21verified2026-10-17 · 2026-10-21open
magic cat2χ ≤ 1——verified2021-06-14 · 2026-09-24open
magic cat3χ = 2verified2026-09-24verified2021-06-14 · 2026-09-24settled
magic cat4χ = 2verified2026-09-24verified2021-06-14 · 2026-09-24settled
magic cat5χ = 3verified2026-10-16 · 2026-09-24verified2021-06-14 · 2026-09-24settled
magic cat6χ = 3verified2026-10-16 · 2026-09-24verified2021-06-14 · 2026-09-24settled
magic cat75 ≤ χ ≤ 6attested2026-10-17 · 2026-10-21verified2021-06-14 · 2026-09-24open
magic cat85 ≤ χ ≤ 6attested2026-10-17 · 2026-10-21verified2021-06-14 · 2026-09-24open

Cost per discovery

Cumulative record-tier bounds and cumulative CPU-hours, by date. Cost is the sum of the compute blocks on the bounds and of every run in the autoresearch log, failed runs included.

050100150200verified bounds170 verified bounds025005000750010000CPU-hours8455.40 CPU-hours09-01 (seeded)09-0709-1209-1509-1809-2109-2410-0210-1210-1610-21
verified bounds, cumulativeCPU-hours, cumulative
dateboundsCPU-hCPU-h per boundmedian declared CPU-hcumulative boundscumulative CPU-h
2026-09-01 and earlier (seeded)380.630.0170.015380.63
2026-09-0720.000.000—400.63
2026-09-1250.000.000—450.63
2026-09-1510.000.000—460.63
2026-09-1670.670.0960.080531.30
2026-09-1710.600.6000.600541.90
2026-09-181318.591.4300.0506720.49
2026-09-19012.32——6732.82
2026-09-2011477.2143.3830.00578510.02
2026-09-2130.040.0130.04081510.06
2026-09-2280.350.0430.00189510.41
2026-09-238124.0015.5010.00197634.42
2026-09-241287.007.2500.001109721.42
2026-09-261121.50121.500121.500110842.92
2026-10-023110.4036.80028.900113953.32
2026-10-1210.000.0010.001114953.32
2026-10-1658.811.7620.010119962.13
2026-10-1729223.417.7040.0001481185.54
2026-10-1810.000.0010.0011491185.54
2026-10-2190.050.0060.0031581185.60
2026-10-23127269.81605.81711.3831708455.40

Median declared CPU-hours is the median of the compute blocks on the bounds dated that day. Bounds without a compute block count as discoveries at no recorded cost; the literature values seeded before 2026-09-01 are folded into the first row.

Per cell

Keyed by orbit, copies and rank, as in autoresearch/summary.py. A solution is an exact refit in the log or a record-tier bound with a compute block.

orbitmrankrunsCPU-hsolutionsCPU-h per solutionon the board
Strange3410.05010.050lean reproduced
Strange5410.01010.010reproduced
Strange5532.70012.700reproduced
Strange5621800.00011800.000attested
Strange5810.00110.001lean
Strange6510.05010.050reproduced
Strange6621800.00011800.000attested
Strange7500.00010.000reproduced
Strange7621800.00011800.000attested
Strange71610.00110.001verified
Strange8500.00010.000reproduced
Strange8621800.00011800.000attested
Strange81510.3330——
Strange81610.00110.001verified
Norrell1210.00110.001verified
Norrell3410.05010.050lean reproduced
Norrell4310.05010.050reproduced
Norrell4537.60017.600reproduced
Norrell46138.100138.100attested
Norrell471121.5001121.500lean attested
Norrell5700.00010.000attested
Norrell51066.00016.000verified
Norrell51210.00110.001verified
Norrell6700.00010.000attested
Norrell61541.1140——
Norrell61610.00110.001verified
H₃1210.00110.001verified
H₃3410.05010.050lean reproduced
H₃4310.05010.050reproduced
H₃4511.40011.400reproduced
H₃46411.602111.602attested
H₃47582.077182.077attested
H₃5700.00010.000attested
H₃51210.00110.001verified
H₃6700.00010.000attested
H₃61541.3550——
H₃61610.00110.001verified
T₃2120.0000——
T₃37654.13814.138verified
T₃384468.7001468.700lean attested
T₃4610.20010.200reproduced
T₃4881.40711.407attested
T₃5610.15010.150reproduced
T₃5800.00010.000attested
T₃51880.60010.600lean
T₃6800.00010.000attested
T₃62710.00110.001verified
H-type1210.00110.001verified
H-type2110.0000——
H-type2210.01010.010lean
H-type3310.01010.010lean reproduced
H-type4430.32430.108lean reproduced
H-type5410.02010.020reproduced
H-type55494.06314.063reproduced
H-type56237.220218.610lean attested
H-type6410.30010.300reproduced
H-type65363.2360——
H-type66274.700174.700lean attested
H-type6730.10010.100verified
H-type7600.00010.000attested
H-type7910.01010.010lean
H-type8600.00010.000attested
H-type81210.01010.010lean
H-type9600.00010.000attested
H-type91810.01010.010verified
H-type10600.00010.000attested
H-type101810.01010.010lean
BK T-type1210.00110.001verified
BK T-type2210.01010.010lean
BK T-type3320.01120.005lean reproduced
BK T-type5310.01010.010reproduced
BK T-type5410.01010.010reproduced
BK T-type55371.91111.911attested
BK T-type56236.401218.200lean attested
BK T-type6410.01010.010reproduced
BK T-type6540.46510.465attested
BK T-type6610.00020.000lean attested
BK T-type7600.00010.000attested
BK T-type7910.00110.001verified
BK T-type8600.00010.000attested
BK T-type8830.4630——
BK T-type8910.00110.001verified
BK T-type9600.00010.000attested
BK T-type91510.00110.001verified
BK T-type10600.00010.000attested
BK T-type101510.00110.001verified
BK T-type101810.00110.001verified
√T1220.00420.002verified
√T2320.00420.002verified
√T3420.00420.002verified
√T4410.00310.003verified
√T4540.02120.011verified
√T5640.02120.011verified
√T6630.02010.020verified
√T67147.000147.000attested
√T61210.00110.001verified
√T7700.00010.000attested
√T7123722.745122.745verified
CS1220.00620.003verified
CS2320.01520.007verified
CS3420.03010.030reproduced
CS3610.00110.001verified
T₅1310.00110.001lean
T₅257613.44026.720lean reproduced
T₅3500.00010.000reproduced
T₅36228.900128.900attested
T₅31510.00110.001lean
T₅4500.00010.000reproduced
T₅4600.00010.000attested
T₅42510.00110.001lean
T₅5600.00010.000attested
T₅57510.00110.001verified
magic cat5330.01010.010verified
magic cat6300.00010.000verified
magic cat7452.80012.800verified
magic cat756111.7001111.700attested
magic cat8400.00010.000verified
magic cat856111.7001111.700attested
T3sector02210.0000——
T3sector02310.0010——
T3sector045727.3840——
T3sector05860.9730——

Evidence index

172 bounds in bounds/: 172 reached main through a pull request, 53 carry a verification receipt matching the file's content hash. By tier: 44 lean, 58 verified, 31 reproduced, 37 attested, 2 cited. Machine-readable copy: evidence_index.json.

boundtierPRmergeaddedreceiptLeancompute
χR(|S⟩⊗1)≥2lean#61fec578fb6a801680d49c 2026-09-20S-m1-lower-2.json staleStrangeM1Lower—
χR(|S⟩⊗1)≤2lean#17c856eab44721f53b5a0e 2026-09-12S-m1-upper-2.json staleM1StabRank—
χR(|S⟩⊗2)≥2lean#19108ccb1d8a3ff6e746a8 2026-09-15—IsStab—
χR(|S⟩⊗2)≤2lean#17c856eab44721f53b5a0e 2026-09-12—IsStab—
χR(|S⟩⊗3)≥4reproduced#17c856eab44721f53b5a0e 2026-09-12S-m3-lower-4.json stale—1 runs, 0.05 CPU-h
χR(|S⟩⊗3)≤4lean#17c856eab44721f53b5a0e 2026-09-12—M3StabRank—
χR(|S⟩⊗4)≥4reproduced#17c856eab44721f53b5a0e 2026-09-12S-m4-lower-4.json stale——
χR(|S⟩⊗4)≤4lean#17c856eab44721f53b5a0e 2026-09-12S-m4-upper-4.json staleTensorStabRank—
χR(|S⟩⊗5)≥4reproduced#378123be156abe6917e6b0 2026-09-18S-m5-lower-4.json stale—1 runs, 0.01 CPU-h
χR(|S⟩⊗5)≥5reproduced#40a3d18db43af44f13ea8b 2026-09-18S-m5-lower-5.json stale—3 runs, 2.7 CPU-h
χR(|S⟩⊗5)≥6attested#187b0cc69b9e7b42f73cccc 2026-10-23S-m5-lower-6.json—2 runs, 1800 CPU-h
χR(|S⟩⊗5)≤8lean#378123be156abe6917e6b0 2026-09-18S-m5-upper-8.json staleStrangeM5StabRank1 runs, 0.001 CPU-h
χR(|S⟩⊗6)≥5reproduced#61fec578fb6a801680d49c 2026-09-20S-m6-lower-5.json stale—1 runs, 0.05 CPU-h
χR(|S⟩⊗6)≥6attested#187b0cc69b9e7b42f73cccc 2026-10-23S-m6-lower-6.json—2 runs, 1800 CPU-h
χR(|S⟩⊗6)≤8lean#17c856eab44721f53b5a0e 2026-09-12S-m6-upper-8.json staleTensorStabRank—
χR(|S⟩⊗7)≥5reproduced#1772fffdf2d28042d19b47e 2026-10-21S-m7-lower-5.json—0 runs, 0 CPU-h
χR(|S⟩⊗7)≥6attested#187b0cc69b9e7b42f73cccc 2026-10-23S-m7-lower-6.json—2 runs, 1800 CPU-h
χR(|S⟩⊗7)≤16verified#1049ce1755563d47094a8e5 2026-09-22S-m7-upper-16.json stale—1 runs, 0.001 CPU-h
χR(|S⟩⊗8)≥5reproduced#1772fffdf2d28042d19b47e 2026-10-21S-m8-lower-5.json—0 runs, 0 CPU-h
χR(|S⟩⊗8)≥6attested#187b0cc69b9e7b42f73cccc 2026-10-23S-m8-lower-6.json—2 runs, 1800 CPU-h
χR(|S⟩⊗8)≤16verified#1049ce1755563d47094a8e5 2026-09-22S-m8-upper-16.json stale—1 runs, 0.001 CPU-h
χR(|N⟩⊗1)≥2verified#1772fffdf2d28dd232c348d 2026-10-21N-m1-lower-2.json——
χR(|N⟩⊗1)≤2verified#1772fffdf2d28dd232c348d 2026-10-21N-m1-upper-2.json—1 runs, 0.001 CPU-h
χR(|N⟩⊗2)≥3lean#18293f15c35bb53bead597 2026-09-12N-m2-lower-3.json staleM2Lower—
χR(|N⟩⊗2)≤3lean#17c856eab44721f53b5a0e 2026-09-12—M2StabRank—
χR(|N⟩⊗3)≥4reproduced#17c856eab44721f53b5a0e 2026-09-12N-m3-lower-4.json stale—1 runs, 0.05 CPU-h
χR(|N⟩⊗3)≤4lean#17c856eab44721f53b5a0e 2026-09-12—M3StabRank—
χR(|N⟩⊗4)≥3reproduced#38b01a821f92b6b7739eb8 2026-09-18N-m4-lower-3.json stale—1 runs, 0.05 CPU-h
χR(|N⟩⊗4)≥5reproduced#424c0d35fc40fc5587f4bb 2026-09-18N-m4-lower-5.json stale—3 runs, 7.6 CPU-h
χR(|N⟩⊗4)≥6attested#1205e37ed6f9fcd2591e76e 2026-09-23N-m4-lower-6.json stale—1 runs, 38.1 CPU-h
χR(|N⟩⊗4)≥7attested#15401da020f7c73931444d8 2026-09-26N-m4-lower-7.json stale—1 runs, 121.5 CPU-h
χR(|N⟩⊗4)≤7lean#17c856eab44721f53b5a0e 2026-09-12—M4StabRank—
χR(|N⟩⊗5)≥7attested#1801b6a01fbe9ed338df27b 2026-10-21N-m5-lower-7.json—0 runs, 0 CPU-h
χR(|N⟩⊗5)≤10verified#171e6c9e5cb929867cf0659 2026-10-17N-m5-upper-10.json stale—6 runs, 6 CPU-h
χR(|N⟩⊗5)≤12verified#1152ce2188bcdbd2b13d4cf 2026-09-23N-m5-upper-12.json stale—1 runs, 0.001 CPU-h
χR(|N⟩⊗6)≥7attested#1801b6a01fbe9ed338df27b 2026-10-21N-m6-lower-7.json—0 runs, 0 CPU-h
χR(|N⟩⊗6)≤16verified#1152ce2188bcdbd2b13d4cf 2026-09-23N-m6-upper-16.json stale—1 runs, 0.001 CPU-h
χR(|H3⟩⊗1)≥2verified#1772fffdf2d28dd232c348d 2026-10-21H3-m1-lower-2.json——
χR(|H3⟩⊗1)≤2verified#1772fffdf2d28dd232c348d 2026-10-21H3-m1-upper-2.json—1 runs, 0.001 CPU-h
χR(|H3⟩⊗2)≥3lean#18293f15c35bb53bead597 2026-09-12H3-m2-lower-3.json staleM2Lower—
χR(|H3⟩⊗2)≤3lean#17c856eab44721f53b5a0e 2026-09-12—M2StabRank—
χR(|H3⟩⊗3)≥4reproduced#17c856eab44721f53b5a0e 2026-09-12H3-m3-lower-4.json stale—1 runs, 0.05 CPU-h
χR(|H3⟩⊗3)≤4lean#17c856eab44721f53b5a0e 2026-09-12—M3StabRank—
χR(|H3⟩⊗4)≥3reproduced#38b01a821f92b6b7739eb8 2026-09-18H3-m4-lower-3.json stale—1 runs, 0.05 CPU-h
χR(|H3⟩⊗4)≥5reproduced#55517edd3c5b0376132f65 2026-09-18H3-m4-lower-5.json stale—1 runs, 1.4 CPU-h
χR(|H3⟩⊗4)≥6attested#118ae2c6b993aaea775a1e2 2026-09-23H3-m4-lower-6.json stale—1 runs, 11.2 CPU-h
χR(|H3⟩⊗4)≥7attested#161d3d386edcb5797ab339c 2026-10-01H3-m4-lower-7.json stale—1 runs, 81.5 CPU-h
χR(|H3⟩⊗4)≤8lean#17c856eab44721f53b5a0e 2026-09-12H3-m4-upper-8.json staleH3M4StabRank—
χR(|H3⟩⊗5)≥7attested#1790ee13cc9fc97e913306b 2026-10-21H3-m5-lower-7.json—0 runs, 0 CPU-h
χR(|H3⟩⊗5)≤12verified#1152ce2188bcdbd2b13d4cf 2026-09-23H3-m5-upper-12.json stale—1 runs, 0.001 CPU-h
χR(|H3⟩⊗6)≥7attested#1790ee13cc9fc97e913306b 2026-10-21H3-m6-lower-7.json—0 runs, 0 CPU-h
χR(|H3⟩⊗6)≤16verified#1152ce2188bcdbd2b13d4cf 2026-09-23H3-m6-upper-16.json stale—1 runs, 0.001 CPU-h
χR(|T3⟩⊗1)≥3lean#19108ccb1d8a9c7e34e6fc 2026-09-16T3-m1-lower-3.json staleT3M1StabRank—
χR(|T3⟩⊗1)≤3lean#17c856eab44721f53b5a0e 2026-09-12T3-m1-upper-3.json staleM1StabRank—
χR(|T3⟩⊗2)≥3lean#17c856eab44721f53b5a0e 2026-09-12T3-m2-lower-3.json staleT3GaloisM—
χR(|T3⟩⊗2)≤3lean#17c856eab44721f53b5a0e 2026-09-12—T3M2StabRank—
χR(|T3⟩⊗3)≥6reproduced#17c856eab447a9a3425986 2026-09-12T3-m3-lower-6.json stale——
χR(|T3⟩⊗3)≥7verified#410c4c8fefb1263a82903a 2026-09-18T3-m3-lower-7.json stale—2 runs, 0.15 CPU-h
χR(|T3⟩⊗3)≥8attested#62f426dcd36d937e5c4b7c 2026-09-20T3-m3-lower-8.json stale—4 runs, 468.7 CPU-h
χR(|T3⟩⊗3)≤8lean#17c856eab44721f53b5a0e 2026-09-12T3-m3-upper-8.json staleT3M3StabRank—
χR(|T3⟩⊗4)≥6reproduced#247e72a78cef19fd51cfa2 2026-09-16T3-m4-lower-6.json stale—1 runs, 0.2 CPU-h
χR(|T3⟩⊗4)≥8attested#76719ffdd8544e0e378c86 2026-09-20T3-m4-lower-8.json stale—0 runs, 0 CPU-h
χR(|T3⟩⊗4)≤9lean#17c856eab44721f53b5a0e 2026-09-12T3-m4-upper-9.json staleT3M4StabRank—
χR(|T3⟩⊗5)≥6reproduced#30e9d39c1ab5e0f69b94e4 2026-09-18T3-m5-lower-6.json stale—1 runs, 0.15 CPU-h
χR(|T3⟩⊗5)≥8attested#7754bddb896e9b73208a0c 2026-09-20T3-m5-lower-8.json stale—0 runs, 0 CPU-h
χR(|T3⟩⊗5)≤18lean#287218b4219745e4728041 2026-09-17T3-m5-upper-18.json staleT3M5StabRank8 runs, 0.6 CPU-h
χR(|T3⟩⊗6)≥8attested#18108e62371700a64f225e1 2026-10-21T3-m6-lower-8.json—0 runs, 0 CPU-h
χR(|T3⟩⊗6)≤27verified#1152ce2188bcdbd2b13d4cf 2026-09-23T3-m6-upper-27.json stale—1 runs, 0.001 CPU-h
χR(|H⟩⊗1)≥2verified#1772fffdf2d28dd232c348d 2026-10-21qubit_H-m1-lower-2.json——
χR(|H⟩⊗1)≤2verified#1772fffdf2d28dd232c348d 2026-10-21qubit_H-m1-upper-2.json—1 runs, 0.001 CPU-h
χR(|H⟩⊗2)≥2lean#61fec578fb6a801680d49c 2026-09-20qubit_H-m2-lower-2.json staleQubitM2Lower—
χR(|H⟩⊗2)≤2lean#17c856eab44721f53b5a0e 2026-09-12qubit_H-m2-upper-2.json staleQubitHStabRank1 runs, 0.01 CPU-h
χR(|H⟩⊗3)≥3reproduced#18293f15c35b2fad4bd181 2026-09-12qubit_H-m3-lower-3.json stale——
χR(|H⟩⊗3)≤3lean#17c856eab44721f53b5a0e 2026-09-12qubit_H-m3-upper-3.json staleQubitHStabRank1 runs, 0.01 CPU-h
χR(|H⟩⊗4)≥3reproduced#18293f15c35b2fad4bd181 2026-09-12qubit_H-m4-lower-3.json stale——
χR(|H⟩⊗4)≥4reproduced#247e72a78cef19fd51cfa2 2026-09-16qubit_H-m4-lower-4.json stale—1 runs, 0.3 CPU-h
χR(|H⟩⊗4)≤4lean#17c856eab44721f53b5a0e 2026-09-12qubit_H-m4-upper-4.json staleQubitHStabRank1 runs, 0.01 CPU-h
χR(|H⟩⊗5)≥4reproduced#514e2a9643acec8223833b 2026-09-18qubit_H-m5-lower-4.json stale—1 runs, 0.02 CPU-h
χR(|H⟩⊗5)≥5reproduced#567ecdfa90753fe935de6e 2026-09-18qubit_H-m5-lower-5.json stale—1 runs, 1.9 CPU-h
χR(|H⟩⊗5)≥6attested#125e99761ff5ca8f9488efc 2026-09-23qubit_H-m5-lower-6.json stale—1 runs, 37.2 CPU-h
χR(|H⟩⊗5)≤6lean#234ef357db2ee99b00d204 2026-09-16qubit_H-m5-upper-6.json staleQubitHM5StabRank1 runs, 0.02 CPU-h
χR(|H⟩⊗6)≥4reproduced#17c856eab44721f53b5a0e 2026-09-12qubit_H-m6-lower-4.json stale—1 runs, 0.3 CPU-h
χR(|H⟩⊗6)≥6attested#8924d020a3b48bfb853e19 2026-09-22qubit_H-m6-lower-6.json stale—2 runs, 74.7 CPU-h
χR(|H⟩⊗6)≤6lean#17c856eab44721f53b5a0e 2026-09-12qubit_H-m6-upper-6.json staleQubitHM6StabRank—
χR(|H⟩⊗6)≤7verified#234ef357db2ec1a03fe3f5 2026-09-16qubit_H-m6-upper-7.json stale—3 runs, 0.1 CPU-h
χR(|H⟩⊗7)≥6attested#102940bbc3f50c7155b380c 2026-09-22qubit_H-m7-lower-6.json stale—0 runs, 0 CPU-h
χR(|H⟩⊗7)≤9lean#83e02f5545317b14437ef9 2026-09-21qubit_H-m7-upper-9.json staleQubitHM7StabRank1 runs, 0.01 CPU-h
χR(|H⟩⊗8)≥6attested#102940bbc3f50c7155b380c 2026-09-22qubit_H-m8-lower-6.json stale—0 runs, 0 CPU-h
χR(|H⟩⊗8)≤12lean#83e02f5545317b14437ef9 2026-09-21qubit_H-m8-upper-12.json staleQubitHM8StabRank1 runs, 0.01 CPU-h
χR(|H⟩⊗9)≥6attested#183e83c42477b182cf4a188 2026-10-21qubit_H-m9-lower-6.json—0 runs, 0 CPU-h
χR(|H⟩⊗9)≤18verified#1049ce1755563d47094a8e5 2026-09-22qubit_H-m9-upper-18.json stale—1 runs, 0.01 CPU-h
χR(|H⟩⊗10)≥6attested#102940bbc3f50c7155b380c 2026-09-22qubit_H-m10-lower-6.json stale—0 runs, 0 CPU-h
χR(|H⟩⊗10)≤18lean#83e02f5545317b14437ef9 2026-09-21qubit_H-m10-upper-18.json staleQubitHM10StabRank1 runs, 0.01 CPU-h
χR(|T⟩⊗1)≥2verified#1772fffdf2d28dd232c348d 2026-10-21qubit_T-m1-lower-2.json——
χR(|T⟩⊗1)≤2verified#1772fffdf2d28dd232c348d 2026-10-21qubit_T-m1-upper-2.json—1 runs, 0.001 CPU-h
χR(|T⟩⊗2)≥2lean#61fec578fb6a801680d49c 2026-09-20qubit_T-m2-lower-2.json staleQubitM2Lower—
χR(|T⟩⊗2)≤2lean#234ef357db2ec1a03fe3f5 2026-09-16qubit_T-m2-upper-2.json staleQubitTStabRank1 runs, 0.01 CPU-h
χR(|T⟩⊗3)≥3reproduced#247e72a78cef19fd51cfa2 2026-09-16qubit_T-m3-lower-3.json stale—1 runs, 0.001 CPU-h
χR(|T⟩⊗3)≤3lean#234ef357db2ec1a03fe3f5 2026-09-16qubit_T-m3-upper-3.json staleQubitTStabRank1 runs, 0.01 CPU-h
χR(|T⟩⊗4)≥3reproduced#18293f15c35b2fad4bd181 2026-09-12qubit_T-m4-lower-3.json stale——
χR(|T⟩⊗4)≤3lean#17c856eab44721f53b5a0e 2026-09-12—QubitTM4StabRank—
χR(|T⟩⊗5)≥3reproduced#378123be156abe6917e6b0 2026-09-18qubit_T-m5-lower-3.json stale—1 runs, 0.01 CPU-h
χR(|T⟩⊗5)≥4reproduced#397daa655cb3f85b915cc1 2026-09-18qubit_T-m5-lower-4.json stale—1 runs, 0.01 CPU-h
χR(|T⟩⊗5)≥5attested#127bf2bd2f567ad89d8623f 2026-09-23qubit_T-m5-lower-5.json stale—1 runs, 0.002 CPU-h
χR(|T⟩⊗5)≥6attested#132385fd48af6a10a9e6e6b 2026-09-24qubit_T-m5-lower-6.json stale—1 runs, 36.4 CPU-h
χR(|T⟩⊗5)≤6lean#378123be156abe6917e6b0 2026-09-18qubit_T-m5-upper-6.json staleQubitTM5StabRank1 runs, 0.001 CPU-h
χR(|T⟩⊗6)≥4reproduced#61fec578fb6a801680d49c 2026-09-20qubit_T-m6-lower-4.json stale—1 runs, 0.01 CPU-h
χR(|T⟩⊗6)≥5attested#127bf2bd2f567ad89d8623f 2026-09-23qubit_T-m6-lower-5.json stale—0 runs, 0 CPU-h
χR(|T⟩⊗6)≥6attested#132385fd48af6a10a9e6e6b 2026-09-24qubit_T-m6-lower-6.json stale—0 runs, 0 CPU-h
χR(|T⟩⊗6)≤6lean#17c856eab44721f53b5a0e 2026-09-12qubit_T-m6-upper-6.json staleQubitTM6StabRank—
χR(|T⟩⊗7)≥6attested#1845597aeb6bc27a27e7634 2026-10-21qubit_T-m7-lower-6.json—0 runs, 0 CPU-h
χR(|T⟩⊗7)≤9verified#1772fffdf2d28c302c75c9c 2026-10-21qubit_T-m7-upper-9.json—1 runs, 0.001 CPU-h
χR(|T⟩⊗8)≥6attested#1845597aeb6bc27a27e7634 2026-10-21qubit_T-m8-lower-6.json—0 runs, 0 CPU-h
χR(|T⟩⊗8)≤9verified#1049ce1755563d47094a8e5 2026-09-22qubit_T-m8-upper-9.json stale—1 runs, 0.001 CPU-h
χR(|T⟩⊗9)≥6attested#1845597aeb6bc27a27e7634 2026-10-21qubit_T-m9-lower-6.json—0 runs, 0 CPU-h
χR(|T⟩⊗9)≤15verified#1772fffdf2d28c302c75c9c 2026-10-21qubit_T-m9-upper-15.json—1 runs, 0.001 CPU-h
χR(|T⟩⊗10)≥6attested#1845597aeb6bc27a27e7634 2026-10-21qubit_T-m10-lower-6.json—0 runs, 0 CPU-h
χR(|T⟩⊗10)≤15verified#163aaff4fc481eb02bf3e56 2026-10-12qubit_T-m10-upper-15.json stale—1 runs, 0.001 CPU-h
χR(|T⟩⊗10)≤18verified#1049ce1755563d47094a8e5 2026-09-22qubit_T-m10-upper-18.json stale—1 runs, 0.001 CPU-h
χR(|T⟩⊗1)≥2verified#185c0db0bc217f544b56904 2026-10-21qubit_sqrtT-m1-lower-2.json—1 runs, 0.003 CPU-h
χR(|T⟩⊗1)≤2verified#185c0db0bc217f544b56904 2026-10-21qubit_sqrtT-m1-upper-2.json—1 runs, 0.001 CPU-h
χR(|T⟩⊗2)≥3verified#185c0db0bc217f544b56904 2026-10-21qubit_sqrtT-m2-lower-3.json—1 runs, 0.003 CPU-h
χR(|T⟩⊗2)≤3verified#185c0db0bc217f544b56904 2026-10-21qubit_sqrtT-m2-upper-3.json—1 runs, 0.001 CPU-h
χR(|T⟩⊗3)≥4verified#185c0db0bc217f544b56904 2026-10-21qubit_sqrtT-m3-lower-4.json—1 runs, 0.003 CPU-h
χR(|T⟩⊗3)≤4verified#185c0db0bc217f544b56904 2026-10-21qubit_sqrtT-m3-upper-4.json—1 runs, 0.001 CPU-h
χR(|T⟩⊗4)≥4verified#185c0db0bc217f544b56904 2026-10-21qubit_sqrtT-m4-lower-4.json—1 runs, 0.003 CPU-h
χR(|T⟩⊗4)≥5verified#18968e582eb02e2ff283573 2026-10-24qubit_sqrtT-m4-lower-5.json—3 runs, 0.02 CPU-h
χR(|T⟩⊗4)≤5verified#185c0db0bc217f544b56904 2026-10-21qubit_sqrtT-m4-upper-5.json—1 runs, 0.001 CPU-h
χR(|T⟩⊗5)≥6verified#18968e582eb02e2ff283573 2026-10-24qubit_sqrtT-m5-lower-6.json—3 runs, 0.02 CPU-h
χR(|T⟩⊗5)≤6verified#18968e582eb02e2ff283573 2026-10-24qubit_sqrtT-m5-upper-6.json—1 runs, 0.001 CPU-h
χR(|T⟩⊗6)≥6verified#18968e582eb02e2ff283573 2026-10-24qubit_sqrtT-m6-lower-6.json—3 runs, 0.02 CPU-h
χR(|T⟩⊗6)≥7attested#18968e582eb02e2ff283573 2026-10-24qubit_sqrtT-m6-lower-7.json—1 runs, 47 CPU-h
χR(|T⟩⊗6)≤12verified#18968e582eb02e2ff283573 2026-10-24qubit_sqrtT-m6-upper-12.json—1 runs, 0.001 CPU-h
χR(|T⟩⊗7)≥7attested#18968e582eb02e2ff283573 2026-10-24qubit_sqrtT-m7-lower-7.json—0 runs, 0 CPU-h
χR(|T⟩⊗7)≤12verified#18968e582eb02e2ff283573 2026-10-24qubit_sqrtT-m7-upper-12.json—37 runs, 22.7452 CPU-h
χR(|CS⟩⊗1)≥2verified#185c0db0bc217f544b56904 2026-10-21CS-m1-lower-2.json—1 runs, 0.005 CPU-h
χR(|CS⟩⊗1)≤2verified#185c0db0bc217f544b56904 2026-10-21CS-m1-upper-2.json—1 runs, 0.001 CPU-h
χR(|CS⟩⊗2)≥3verified#185c0db0bc217f544b56904 2026-10-21CS-m2-lower-3.json—1 runs, 0.005 CPU-h
χR(|CS⟩⊗2)≤3verified#185c0db0bc217f544b56904 2026-10-21CS-m2-upper-3.json—1 runs, 0.01 CPU-h
χR(|CS⟩⊗3)≥3verified#185c0db0bc217f544b56904 2026-10-21CS-m3-lower-3.json——
χR(|CS⟩⊗3)≥4reproduced#185c0db0bc217f544b56904 2026-10-21CS-m3-lower-4.json—2 runs, 0.03 CPU-h
χR(|CS⟩⊗3)≤6verified#185c0db0bc217f544b56904 2026-10-21CS-m3-upper-6.json—1 runs, 0.001 CPU-h
χR(|T5⟩⊗1)≥3lean#84b45e9f8894df562d18db 2026-09-21T5-m1-lower-3.json staleT5M1StabRank—
χR(|T5⟩⊗1)≤3lean#84b45e9f8894df562d18db 2026-09-21T5-m1-upper-3.json staleT5M1StabRank1 runs, 0.001 CPU-h
χR(|T5⟩⊗2)≥5reproduced#84b45e9f8894df562d18db 2026-09-21T5-m2-lower-5.json stale—2 runs, 0.04 CPU-h
χR(|T5⟩⊗2)≤5lean#13870fffa0113adc82188a6 2026-09-24—T5M2StabRank74 runs, 13.4 CPU-h
χR(|T5⟩⊗2)≤8lean#84b45e9f8894df562d18db 2026-09-21T5-m2-upper-8.json staleT5M2StabRank2 runs, 0.1513 CPU-h
χR(|T5⟩⊗3)≥5reproduced#13870fffa011321ac4ab44e 2026-09-24T5-m3-lower-5.json stale—0 runs, 0 CPU-h
χR(|T5⟩⊗3)≥6attested#162790bf24279f325934dbe 2026-10-01T5-m3-lower-6.json stale—2 runs, 28.9 CPU-h
χR(|T5⟩⊗3)≤15lean#13870fffa0113adc82188a6 2026-09-24—T5M3StabRank1 runs, 0.001 CPU-h
χR(|T5⟩⊗4)≥5reproduced#13870fffa011321ac4ab44e 2026-09-24T5-m4-lower-5.json stale—0 runs, 0 CPU-h
χR(|T5⟩⊗4)≥6attested#162790bf24279f325934dbe 2026-10-01T5-m4-lower-6.json stale—0 runs, 0 CPU-h
χR(|T5⟩⊗4)≤25lean#13870fffa0113adc82188a6 2026-09-24—T5M4StabRank1 runs, 0.001 CPU-h
χR(|T5⟩⊗5)≥6attested#182c8156efbd90c278d2955 2026-10-21T5-m5-lower-6.json—0 runs, 0 CPU-h
χR(|T5⟩⊗5)≤75verified#1772fffdf2d285a03130789 2026-10-21T5-m5-upper-75.json—1 runs, 0.001 CPU-h
χR(|cat2⟩)≤1verified#14117b9c1f584e84a236183 2026-09-24cat-m2-upper-1.json stale——
χR(|cat3⟩)≥2verified#14117b9c1f584e84a236183 2026-09-24cat-m3-lower-2.json stale——
χR(|cat3⟩)≤2verified#14117b9c1f584e84a236183 2026-09-24cat-m3-upper-2.json stale——
χR(|cat4⟩)≥2verified#14117b9c1f584e84a236183 2026-09-24cat-m4-lower-2.json stale——
χR(|cat4⟩)≤2verified#14117b9c1f584e84a236183 2026-09-24cat-m4-upper-2.json stale——
χR(|cat5⟩)≥3verified#14117b9c1f584e84a236183 2026-09-24cat-m5-lower-3.json stale—3 runs, 0.01 CPU-h
χR(|cat5⟩)≤3verified#14117b9c1f584e84a236183 2026-09-24cat-m5-upper-3.json stale——
χR(|cat6⟩)≥3verified#14117b9c1f584e84a236183 2026-09-24cat-m6-lower-3.json stale—0 runs, 0 CPU-h
χR(|cat6⟩)≤3verified#14117b9c1f584e84a236183 2026-09-24cat-m6-upper-3.json stale——
χR(|cat7⟩)≥3cited#14117b9c1f584e84a236183 2026-09-24———
χR(|cat7⟩)≥4verified#1707bf45fea9e22939a2cff 2026-10-16cat-m7-lower-4.json stale—5 runs, 2.8 CPU-h
χR(|cat7⟩)≥5attested#178a3f179f75237dbae0828 2026-10-21cat-m7-lower-5.json—6 runs, 111.7 CPU-h
χR(|cat7⟩)≤6verified#14117b9c1f584e84a236183 2026-09-24cat-m7-upper-6.json stale——
χR(|cat8⟩)≥3cited#14117b9c1f584e84a236183 2026-09-24———
χR(|cat8⟩)≥4verified#1707bf45fea9e22939a2cff 2026-10-16cat-m8-lower-4.json stale—0 runs, 0 CPU-h
χR(|cat8⟩)≥5attested#178a3f179f75237dbae0828 2026-10-21cat-m8-lower-5.json—6 runs, 111.7 CPU-h
χR(|cat8⟩)≤6verified#14117b9c1f584e84a236183 2026-09-24cat-m8-upper-6.json stale——

A bound with no pull request was added to main directly; its adding commit is the provenance. A receipt is certs/<slug>.json, written by the verifier and keyed to the content hash of the submission file, so an edited bound shows a stale receipt until it is re-verified. Lean-tier bounds have their receipt under certs/lean-<module>.json instead.

Reproducing this page

make build                       # re-verifies every bound without a receipt
uv run --extra challenge python site_challenge/build.py --no-verify
uv run --extra challenge python autoresearch/summary.py --since 2026-09-15

The second command rebuilds the pages from docs/ledger.json and the receipts in certs/ without running any certificate; a bound with neither is listed above as unverified and left off the board.